Earlier today I set you this puzzle about an imaginary game show.

At the end of the show two people will be chosen and each placed in a separate booth.

In the booth, each of them will flip a fair coin, out of sight of the other person but visible to the audience.

Then each of them must guess what the other person flipped—heads or tails. If they both guess correctly, they receive a prize.

The chance of each person guessing correctly is 50 per cent. So the chance of both guessing is 25 per cent.

Or is it?

You’re in the studio watching the show, and to your surprise, you and your friend are called up to play the game. As you walk up to the stage, you whisper a strategy to your companion that gives you a better than 25% chance of winning the prize. What is this strategy, and what is the probability of winning?

Solution:

Remarkably, if each of you announces the result of your own coin flip you will raise your probability of winning to 50 per cent!

The four equally likely outcomes of two flips are HH, TH, HT and TT.

You will both flip the same value (HH, or TT) 50 per cent of the time, and when you do you will both have predicted the other person’s flip, and therefore win the prize.

Alternatively, you could each agree to guess that the other has flipped the opposite of your own flip. The odds work out the same.

I hope you enjoyed today’s puzzle. I’ll be back in two weeks.

Thanks to Henk Tijms for today’s puzzle. Henk is Emeritus Professor of Operations Research at VU Amsterdam and the author of several books on probability.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.